The present invention relates to automatic control systems. It applies both to closed-loop (feedback) systems and to open-loop systems.
A basic problem in the design of automatic control systems is that of speed of response. The designer normally knows the idealized response that is desired from each particular type of input and he frequently works with systems that are sufficiently close to linear to permit the superposition of combined inputs to produce combined responses thereto. However, physical limitations upon the equipment frequently lead to the introduction of delays between the desired output signal and the observed output signal. This is especially true in the case of the linear second-order system which is typical of a wide range of automatic control systems and which provides an adequate descriptive approximation to the performance of still more such systems. The second-order system is describable by a linear differential equation of the second order with constant coefficients. Alternatively, it is characterized in the s-plane by a pair of poles. Such a system may be in one of two conditions: it may be either overdamped or oscillatory, with a dividing line between the two comprising the case of critical damping. The overdamped condition is characterized by a step response that comprises the sum of two exponentials with different time constants. In the s-plane the overdamped condition is represented by two poles on the negative real axis. The exponential having the longer time constant represents a delay between the actual value and the final value of the output that is often undesirable from the standpoint of the designer. Typically the designer would like to see a close approximation to a step output in response to a step input. However, if he varies system constants to vary the location of the poles in an overdamped system so as to reduce the time constant of the dominant exponential term, he approaches more closely the oscillatory condition which may be undesirable for a number of reasons. For example, nonlinearities in the system may tend to sustain any oscillations that are started. The relocation of poles or, in other words, the variation of the time constants of exponentials in the step response of the linear second order system thus involves compromises that may have undesirable results. It would be useful to have a system for controlling response to a step input that does not require a change in the damping of the system.
It is not always desirable to have an overdamped system. Sometimes a designer makes the choice of a system exhibiting an underdamped or oscillatory response. Such a system responds to a step input by overshooting the final value and oscillating with a damped oscillation about this final value. The amount of the overshoot and the frequency and rate of damping of the oscillation are functions of the system parameters. Two commonly applied figures of merit for systems that exhibit overshoot are the peak overshoot and the settling time. The peak overshoot is often expressed on a percent or a per unit basis as a measure of the ratio of the height of the first overshoot above the final value to the height of the final value for a step input. The settling time is defined as the time required for oscillations to decrease to a specified absolute percentage of the final value and thereafter remain less than this value. It is common to specify the allowable percentage as 2% or 5%. These figures are arbitrarily chosen design criteria. Each provides a figure of merit in comparing systems for their ability to produce a desired output from a given input. Generally speaking, rapid response of a system to a changing input is assocated with oscillations about the final value following the change and slowness of response is associated with increased damping that removes such oscillations. In a linear system and, to a lesser degree, in nonlinear systems, part of the design problem includes a compromise between the desired degree of rapidity of response and the tolerable amount of oscillation about a final value.
The foregoing discussion has been cast primarily in terms of a so-called type-zero system. This is a system in which the steady-state response to a step input is a constant value. Such a system follows a ramp input with an error that increases in time and similarly produces an infinite steady-state error in response to a parabolic input. The same conclusions, though, hold for systems characterized by higher type numbers. For example, the type-one system has a step response that provides zero error in the steady state and provides a constant error in the steady state in response to a ramp input. The type-two system produces zero steady-state error in response to both a step and a ramp input and produces a constant error in response to a parabolic input. It can be seen by inspection that increasing the number of the system type increases the amount of integration in the circuit and thereby enables the circuit to follow a higher-order input signal. These systems have in common the fact that selection of the system parameters and determination of whatever compensation may be necessary in either a forward loop or a feedback loop determines the response of the system to any given class of signals. Improvement of this response in one area generally results in deterioration in another area. For example, improving the speed of response generally produces an increase in any oscillation that exists about the final value and hence increases the time necessary to produce settling within a given percent variation from the final value.
One method of overcoming the disadvantages inherent in dealing with a fixed-parameter control system is to condition the input signal to the system. The general result of such a process is to produce in the conditioning signal a correction value that is a function of the signal itself. Such a signal is also a function of the system constants. The method of generating and applying such signals will require information as to current input signals and it must be based upon the parameters of the system.
It is an object of the present invention to improve the performance of control systems.
It is a further object of the present invention to produce a modified signal to replace the input signal to a control system so as to result in improved response.
It is further object of the present invention to provide a corrective signal to add to the input signal to a system to provide an improved response to the original signal.
It is a further object of the present invention to provide an improved response for sampled-data control systems.
It is a further object of the present invention to provide means for calculating and applying a corrective signal to be added to the signal present in a sample-data control system to provide an improved response of the system.
It is a further object of the present invention to provide means for calculating a signal correction that can be varied from time to time as system parameters change to produce a modified signal to supplement the input signal to the system and thus provide an adaptive version of improved system response.
It is a further object of the present invention to provide means allowing the use of underdamped systems and systems having high gain while maintaining stability of the system by calculating correction signals to be added to or used to supplement the input signals to the system to provide improved system response.
It is a further object of the present invention to provide an improvement in the response of an open-loop system by calculating a correction signal to be used in conjunction with the input signal to the open-loop system.
Other objects of the invention will become apparent in the course of the detailed description of the invention.